This journal is c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 14527–14533 14527

Electrostatic attraction between a hydrophilic solid and a bubblew

Li Jiang,aMarta Krasowska,

aDaniel Fornasiero,

aPeter Koh

band John Ralston*

a

Received 30th July 2010, Accepted 7th September 2010

DOI: 10.1039/c0cp01367f

The contact between fine hydrophilic a-Al2O3 particles and nitrogen bubbles was studied as a

function of solution composition in single bubble capture experiments, where the bubble collection

efficiency was measured. The surface charges of both bubble and particle were controlled by varying

the electrolyte concentration and pH of the solution. In all experiments the bubbles were negatively

charged while the a-Al2O3 particles were either negatively (above pH of the isoelectric point, pHIEP)

or positively (below pHIEP) charged. The collection efficiency was found to be strongly influenced

by the surface charge of the particles. The maximum collection efficiency occurred when the bubble

and particle were oppositely charged (at low pH values) and at low salt concentration, i.e. when a

long range attractive electrostatic interaction is present. In the case where both bubble and particle

were of the same charge, the collection efficiency was near to zero within experimental error and

was not influenced by either salt concentration or pH. This is the first experimental proof of the

concept of ‘contactless flotation’, first proposed by Derjaguin and Dukhin in 1960, with far

reaching implications from minerals processing to biology.

Introduction

The interaction between gas bubbles and particles is critical for

various processes that occur in mineral processing and waste

water treatment, as well as in the food, cosmetic and pharma-

ceutical industries. In mineral processing, flotation is used

to separate mineral particles, with selectivity controlled by

differences in surface wettability.1 During flotation, as the

particles approach a gas bubble, three fundamental processes

determine whether or not the bubble–particle(s) aggregate can

be formed. These are collision, attachment and detach-

ment. The three sub-processes are dominated by long-

range hydrodynamic interactions (collision), surface forces

(attachment) and capillary forces (detachment).2,3 Overall,

successful flotation is manifested by a high collection

efficiency, Ecoll, of floated particles. The collection efficiency

can be expressed as:4

Ecoll = Ec � Ea � Es (1)

where Ec is the collision efficiency, Ea is the attachment

efficiency and Es is the stability efficiency of the particle–bubble

aggregate. Amongst these three sub-processes, Ec and Es are

well-described by existing models. Ec models have been proposed

for both clean (mobile) and contaminated (immobile) bubble

surfaces. The Generalized Sutherland Equation (GSE)5–7

describes the first case, while the Sutherland,8 Yoon–Luttrell9

and Schulze10 models describe the latter. Es is well-described

by the Schulze approach.11 According to Derjaguin et al.,12

the Es for small particles is unity, as is the case for the present

study where only very small particles (diameters between

B0.5–2.5 mm) have been used. However, our understanding

for Ea is incomplete. There have been various kinetic and

thermodynamic approaches to describe Ea. From a kinetic

perspective, Dobby and Finch13 proposed an equation of Ea

which is the ratio of two projected areas, representing areas

associated with the successful attachment and non-attachment

of a particle with a bubble during sliding:14

Ea-DF ¼sin2 yasin2 yt

ð2Þ

where ya is the attachment or adhesion angle:

ya ffi 2 arctan exp �tindvb 1þ 1

2Rb

RpþRb

� �3� �

Rp þ Rb

8>><>>:

9>>=>>;

ð3Þ

and yt is the angle of tangency:

yt ¼ arcsin 2bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ b2 � b

q� �� �1=2ð4Þ

where b is a dimensionless number, expressed as:

b ¼ 4Ec-SU

9K3ð5Þ

Ec-SU is the collision efficiency, calculated according to

Sutherland model:

Ec-SU ¼3dp

dbð6Þ

with the dimensionless number K3 defined as:

K3 ¼vbðrp � rfÞd2

p

9Zdbð7Þ

where vb is the bubble rising velocity, rp and rf are the densityfor particle and fluid, Z is the fluid viscosity, whilst db and dp

a Ian Wark Research Institute, University of South Australia,Mawson Lakes, SA 5095, Australia.E-mail: john.ralston@unisa.edu.au; Fax: +61 8 8302 3683;Tel: +61 8 8302 3066

bCSIRO Mathematics, Informatics and Statistics, Clayton,VIC 3168, Australia

w Electronic supplementary information (ESI) available: XRD patternsand SFM images. See DOI: 10.1039/c0cp01367f

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

14528 Phys. Chem. Chem. Phys., 2010, 12, 14527–14533 This journal is c the Owner Societies 2010

are the bubble and particle diameters, respectively. The only

unknown parameter in eqn (3) is the induction time (tind). The

induction time may be expressed as follows:

tind = tfd + tfr + ttpcl (8)

where tfd refers to film drainage time, tfr is the film rupture

time and ttpcl is the time for the formation of a stable three

phase contact line (TPCL). The induction time is linked to

particle size14–17 by the empirical equation:

tind = A�dBp (9)

where dp is particle diameter and both A and B are dimension-

less parameters. For hydrophobic particles, parameter A

depends on particle contact angle, bubble size and ionic strength

while parameter B is independent of these factors.14–17 The

determination of A and B for hydrophilic particles will be

discussed below.

From a thermodynamic point of view Scheludko et al.18

suggested that small particles do not have enough kinetic

energy to rupture the thin liquid film between a bubble and

particle, therefore a wetting perimeter cannot be formed, i.e.

they do not attach and thus do not float. However, Derjaguin

et al.12 pointed out that the formation of a TPCL and a stable

wetting perimeter is not necessary for the attachment of fine

particles, for they can be ‘‘fixed’’ at a gas bubble surface due to

long range electrostatic attraction. Such a process is referred to

as ‘‘contactless flotation’’ and has the potential to recover fine

hydrophilic particles.

The investigation of the electrostatic interaction between a

gas bubble and a hydrophilic solid surface has been mainly

focused on solids with isoelectric points at low pH. These

include quartz,19,20 mica21 with recent work focused on TiO2,

which has a pHIEP at intermediate pH values.22,23 Apart from

this isolated titania case, all the reported investigations were

carried out only at pH values above the pHIEP of the solid.

Since both gas bubbles (1.5–2.5)2 and silicates (2–3)24 have

rather low pHIEP values, both the particle and gas bubble

surfaces were negatively charged. Thus repulsive electrostatic

and van der Waals forces together stabilize the wetting film,

preventing hydrophilic particle attachment to gas bubbles.19

a-Al2O3 has a pHIEP of B925 and the potential and charge

on the surface may be controlled through altering the pH. The

a-Al2O3 surface is thus ideal for probing the interaction of a

gas bubble with a hydrophilic solid whose surface charge can

be changed from positive to negative by altering pH.

In the present study we investigate two cases: (i) when

both bubble and particle bear a negative surface charge

(pH > pHIEP of both particle and bubble), and (ii) when the

bubble is negatively charged (pH > pHIEP) whilst the particle

is positively charged (pH o pHIEP). Thus, both the repulsive

and the attractive electrostatic interactions between a hydro-

philic a-Al2O3 and a gas bubble surface are probed.

Materials and methods

Alumina particles and reagents

The alumina particles used for flotation experiments were

hydrated alumina particles (Hydral 710, Alcoa of Australia

Limited). Potassium chloride (Chem-Supply, 99%, AR)

used for solution preparation was recrystallized and calcined

(8 h at 550 1C) to remove organic impurities. Hydro-

chloric acid (Titrisols, Merck) and potassium hydroxide

(AR, Merck) were used to adjust pH. Nitric acid (69.5%,

AR, Scharlau) and sodium hydroxide (AR, Merck) were used

for alumina particle cleaning. High purity MilliQ water

(Elga UHQ) with a resistance of 18.2 MO cm and a surface

tension of 72.4 mN m�1 at 22 1C was used in all experiments.

High purity nitrogen gas used for bubble generation was

supplied by BOC gases.

To ensure that the alumina particles were hydrophilic,

they were cleaned prior to the experiment. The cleaning

procedure was as follows: (i) particles (10 g) were soaked in

10�3 M HNO3 solution26 for 30 min; (ii) rinsed with MilliQ

water and centrifuged to remove the supernatant; (iii) soaked

in hot 30% NaOH solution; (iv) rinsed copiously with MilliQ

water until the pH of the wash water was 5.8; (v) repeatedly

centrifuged to make sure the particles smaller than 0.5 mmwere eliminated. In all the experiments, the final particle size

distribution measured with an Accusizer 770A (Particle Sizing

Systems, USA) using the light scattering and obscuration was

between 0.5 and 2.5 mm (with maximum at 2.09 mm).

All glassware used in the experiments was cleaned in

1 M KOH solution and rinsed with MilliQ water until the

wash water pH was 5.8.

The crystalline form of alumina was determined by X-ray

diffraction (XRD), using a Co X-ray source (l = 1.7902 A)

(Phillips PW1730) in the angle range from 5 to 901.

The zeta potential for a-Al2O3 particles (size fraction

0.5–1 mm) was determined using a laser light diffraction

technique (Zetasizer Nano ZS, Malvern).

An a-Al2O3 single crystal (0001 crystal plane), (Crystal

Systems Corporation, Japan) was cleaned in the same way

as the a-Al2O3 particles. Contact angles of these cleaned

a-Al2O3 single crystals were measured using the captive bubble

technique.27,28 A high purity nitrogen bubble was formed at

the tip of a fine needle and pressed against the a-Al2O3 single

crystal, immersed into solution. The images were captured by

a camera (OCA 20 instrument, Data Physics) and analyzed

with the OCA 20 image profile software.

Single bubble flotation

The experiments were conducted in a modified Hallimond

tube5 shown in Fig. 1. Single bubbles were generated one by

one at the end of a fine steel needle (Hamiltons, USA)

mounted at the base of the column. The diameter of a bubble

(measured with a video camera) was 800 (�50) mm. The

bubble rise velocity measured at the beginning and end of

the experiments was 25 � 1 cm s�1. In all cases bubble velocity

corresponded to that predicted by the Hadamard–Rybczynski

equation, indicating that the bubble surfaces were clean,

with full slip occurring at their surfaces.22,29,30 The distance

between two consecutive bubbles was kept constant (B14 cm),

so as to eliminate turbulence and particle entrainment. The

bottom part of the column was filled with a-Al2O3 suspension

(0.3 w% in KCl), while the top part was filled with the same

background electrolyte, in order to keep both the ionic

This journal is c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 14527–14533 14529

strength and pH constant. For each flotation experiment,

200 single bubbles were released before the concentrate was

collected. Each measurement for a given background electro-

lyte was repeated at least three times. The number of particles

collected in the concentrate was measured with the Accusizer

770A. The experiment was conducted in an extremely clean

system (the number of background counts was less than 30 per

ml—this value was subtracted from the collection data). The

experimental error was lower than 10%.

The particle–bubble collection efficiency, Ecoll, is defined as:5

Ecoll ¼Npf

PNCphsðdp þ dbÞ2=4ð10Þ

where Npf is the number of particles collected per bubble, PNC

is the number of particles per cm�3 of feed suspension, hs is the

height of suspension, dp and db are particle and bubble

diameters, respectively. As mentioned above, Es for fine

particles is unity,12 therefore the ‘experimental’ Ea values

may be calculated from eqn (11):

Ea ¼Ecoll

Ec-GSEð11Þ

where the Ec-GSE is the collection efficiency calculated from the

GSE model.5 The GSE collision model was chosen to represent

Ec in eqn (11), following the successful application of this

collision model5,31 for silica particles with diameters between

7–60 mm and contact angles up to 701 in a wide range of

electrolyte concentration and bubble size. The GSE model

incorporates both the positive effect of the hydrodynamic

pressing force, I1, and the negative effect of centrifugal force,

I2, on the particle–bubble collision for a mobile bubble surface

and is given by:5

Ec-GSE = Ec-SU sin2yt exp(I1 + I2) (12)

I1 ¼ 3K3 cos yt ln3

Ec-SU� 1:8

� �ð13Þ

I2 ¼ �4 cos yt

2

3þ cos3 yt

3� cos yt

� �

sin4 ytð14Þ

The GSE is valid for potential flow conditions (80oReo 500),10

and applies to the present system with Re E 200.

Results and discussion

Alumina particles characterization

The X-ray diffraction pattern of Al2O3 particles (presented

in ESIw in Fig. 1(A)) shows excellent agreement with the

Siroquant V3 library XRD spectrum for a-phase Al2O3 with

a characteristic diffraction peak at 21.401. The scanning

electron microscope (SEM, PHILIPS XL30) image of a-Al2O3

particles (presented in ESIw in Fig. 1(B)) shows that the particles

are hexagonal in shape.

The zeta potential data for a-Al2O3 particles are presented

in Fig. 2. The pHIEP is located at pHE 9.1. The pHIEP value is

close to that reported by Franks for a-Al2O3 particles.25 The

zeta potential increases in magnitude on either side of the

pHIEP with pH and with decreasing electrolyte concentration.

Since pHIEP is invariant with KCl concentration it is identical

to pHPZC (where PZC is the point of zero charge).

Single bubble collection results—above pHIEP

The Ecoll and Ea data for hydrophilic a-Al2O3 particles are

presented in Fig. 3 at pH 10 (above the pHIEP) as a function of

particle size and KCl concentration. The Ecoll values are very

low (nearly zero) and do not depend on salt concentration.

The Ea values (calculated from Ecoll data and eqn (11)) are also

correspondingly low (nearly zero). At pH values higher than

the pHIEP the total potential of interaction between particle

and bubble is repulsive as both the van der Waal and electro-

static (both the bubble and particle surfaces are negatively

charged) interactions are repulsive. As a result, no particle–

bubble attachment is expected and we can therefore assume

that the very small collection efficiency measured at pH values

higher than the pHIEP of alumina is due to particle entrainment

in the wake behind the rising bubbles. Therefore, collection

efficiencies at pH 10 or particle entrainment at each particle

diameter were subtracted from all the subsequent collection

efficiency data.

Fig. 1 Schematic representation of the apparatus for single bubble

flotation. 1, fine needle; 2, single bubble; 3, three-way tap; 4, overflow

weir; 5, concentrate receiver.15

Fig. 2 Zeta potential of alumina particles as a function of pH and

KCl concentration.

14530 Phys. Chem. Chem. Phys., 2010, 12, 14527–14533 This journal is c the Owner Societies 2010

Single bubble collection results—below pHIEP

The influence of KCl concentration on Ecoll of hydrophilic

a-Al2O3 particles at pH 5.8 is shown in Fig. 4. Ecoll values

are much larger than those above the pHIEP (Fig. 3) and

increase significantly as the salt concentration decreases. For

example for 1.5 mm particles, Ecoll values increased from

14 � 10�5 at 10�2 M KCl to 32 � 10�5 and 50 � 10�5 at

10�3 and 10�4 M KCl, respectively. The trend in Ea with

decreasing KCl concentration is similar to that for Ecoll

(Fig. 4(B)).

The effect of pH at constant salt concentration on Ecoll is

presented in Fig. 5 for 10�4 and 10�2 M KCl. In both cases the

pH exerts a significant effect on Ecoll. For example for 1.5 mmparticles as the pH decreases from 5.8 to 4.5 in 10�4 M KCL,

Ecoll increases from 50� 10�5 to 83� 10�5 while at 10�2 MKCl,

for the same decrease in pH Ecoll only increases from 14 � 10�5

to 20� 10�5 (Fig. 5(B)), which is an order of magnitude less than

at 10�4 M KCl. Similar trends were observed for Ea in Fig. 6(A)

and (B) at 10�4 and 10�2 M KCl, respectively.

Wettability of a-alumina

To verify that the a-Al2O3 surface remained hydrophilic over

the range of pH and salt concentration values studied, a

captive bubble contact angle measurement was conducted on

a cleaned a-Al2O3 plate. The plate was equilibrated in each of

the solutions investigated for five minutes (i.e. a time much

longer than that for the single bubble flotation experiments)

prior to the contact angle measurement. Images of a gas

Fig. 3 Particle–bubble collection (A) and attachment (B) efficiencies

as a function of particle diameter for 800 mm diameter bubbles at

pH 10 in 10�2, 10�3 and 10�4 M KCl solutions.

Fig. 4 Particle–bubble collection (A) and attachment (B) efficiencies

as a function of particle diameter for 800 mm diameter bubbles at

pH 5.8 in 10�2, 10�3 and 10�4 M KCl.

Fig. 5 Particle–bubble collection efficiencies as a function of particle

diameter and pH of the solution for 800 mm diameter bubbles in

(A) 10�4 M KCl, and (B) 10�2 M KCl.

This journal is c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 14527–14533 14531

bubble in contact with the plate taken above and below pHIEP

in Fig. 7 (top) show that there was no film rupture between

bubble and plate, and therefore no attachment occurred.

Similar experiments were performed in a bubble cling test.

No particles were observed clinging to a bubble pressed

against and then lifted from a bed of a-Al2OH3 particles

(Fig. 7, bottom). The presence of edges and points does not

determine the thin film behaviour.

Induction time

As suggested by Dobby and Finch,13,32 tind is the time required

for film drainage, film rupture and TPCL expansion. In this

present case, the thin liquid film between a hydrophilic

a-Al2O3 particle and a gas bubble is stable below and above

pHIEP, therefore it does not rupture and the TPCL cannot be

formed as shown in Fig. 7. Parkinson and Ralston22 showed

that below the pHIEP of a hydrophilic TiO2 surface the thin

liquid film was stable and did not rupture. As a result, tindequals the time of film drainage only. The induction times

calculated from Ea values and eqn (2) to (7) are compared to

those calculated from eqn (9) with values of parameters A and

B in Fig. 8 at different particle diameters and KCl concentra-

tion and pH conditions. The agreement between the two sets

of data is good, especially at low KCl concentrations. The tindvalues, for pH o pHIEP, increase with an increase in KCl

concentration and pH. For example at a particle diameter of

1.5 mm, tind increases from 1.9 to 2.6 ms when KCl concentra-

tion increases from 10�4 to 10�2 M at pH of 5.8, and increases

from 1.6 to 1.9 ms when pH increases from 4.5 to 5.8 at

10�4 M KCl.

According to the literature15 for hydrophobic particles,

parameter A is weakly dependent on salt concentration but

parameter B is not. However, for the hydrophilic particles

investigated in the present study, Fig. 8 shows that both

parameters A and B depend on salt concentration as their

values decrease with increasing salt concentration but also

with increasing pH. For example Fig. 8(A) shows that with

Fig. 6 Particle–bubble attachment efficiencies as a function of

particle diameter and pH of the solution for 800 mm diameter bubbles

in (A) 10�4 M KCl, and (B) 10�2 M KCl.

Fig. 7 Top part: captive bubble contacting a hydrophilic a-Al2O3

plate at pH 3 (below pHIEP) and 10 (above pHIEP) in 10�2 M KCl.

Bottom part: air bubble pressed against and then lifted from a bed

of a-Al2O3 particles (dp > 3 mm) at pH 3 (below pHIEP) and 10

(above pHIEP) in 10�2 M KCl.

Fig. 8 Values of A (A) and B (B) in eqn (9) as a function of salt

concentration and pH of the solution.

14532 Phys. Chem. Chem. Phys., 2010, 12, 14527–14533 This journal is c the Owner Societies 2010

increasing KCl concentration from 10�4 to 10�2 M, the

value of A decreases from 0.04 to 0.012 at a particle diameter

of 1.5 mm.

The values of B obtained in this study for particles between

0.7 to 2.5 mm range from 0.18 to 0.4 (Fig. 8(B)) and therefore

they are in good agreement with previous values of B, 0.4 to

0.8, reported by Dai15 for hydrophobic particles of diameters

between 7 and 60 mm, or those predicted by Jowett16 of 0 for

fine particles, 0 to 3/2 for intermediate particle diameters and

3/2 for coarse particles. Fig. 8(B) also shows that the value of

parameter B decreases significantly with increasing salt con-

centration and slightly with increasing pH (below pHIEP).

Therefore, a higher salt concentration and pH (below pHIEP)

will lead to a longer induction time (Fig. 9), film drainage time,

and consequently result in lower particle bubble attachment

efficiency.

Electrostatic and van der Waals interactions

This study has shown that Ecoll and Ea for the hydrophilic

a-Al2O3 particles are clearly influenced by electrostatic inter-

action between particles and bubbles. To calculate these

electrostatic interactions the linear superposition approxima-

tion (LSA)33 was used:

Ve-LSAðHÞ ¼128pRpRbnikBT

ðRp þ RbÞk2tanh

zecp

4kBT

� �

� tanhzecb

4kBT

� �expð�kHÞ

ð15Þ

where Rp and Rb are particle and bubble radii, kB is the

Boltzmann constant, T is the temperature in Kelvin, e is the

charge of an electron, k is the Debye–Huckel parameter, cp

and cb are the particle and bubble potentials and H is the

distance between particle and bubble surfaces. The potential

for gas bubbles was chosen to be �34 mV and depends only

weakly on salt concentration.15,34 The potential for the

alumina particles was taken from the experimental data shown

in Fig. 2.

The van der Waals interaction can be calculated from:11

VvdwðHÞ ¼ �A132RpRb

6HðRp þ RbÞð16Þ

where A132 is the Hamaker constant for alumina/water/gas

system and was calculated from:11

A12 �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA11A22

pð17Þ

A132 = A12 + A33 � A13 � A23 (18)

where the Hamaker constants for alumina–vacuum–alumina

(A11), gas–vacuum–gas (A22) and water–vacuum–water

(A33) interactions are taken to be 15 � 10�20 J,11 0 J35 and

4.38 � 10�20 J,36 respectively. Using eqn (17) and (18)

the Hamaker constant for alumina–water–gas is found to be

�3.6 � 10�20 J.

The total interaction may be expressed as the sum of

electrostatic and van der Waals interactions. The electrostatic

(eqn (15)), van der Waals (eqn (16)) and total (the sum of both

components) interactions between a hydrophilic a-Al2O3

particle and an air bubble at pH 10 (i.e. above the pHIEP)

and at different salt concentrations are presented in Fig. 10(A).

In all cases both the van der Waals and the electrostatic

interactions are repulsive, which results in a repulsive total

interaction between an a-Al2O3 particle and an air bubble. The

results at pH 5.8 (i.e. below the pHIEP) in Fig. 10(B) show that

the attractive electrostatic interaction is stronger than the van

der Waals interaction, leading to an attractive total interaction

between an a-Al2O3 particle and an air bubble, which increases

in magnitude with decreasing salt concentration.

Therefore, electrostatic interaction controls the ‘‘attachment’’

between a hydrophilic particle and a gas bubble. This

‘‘attachment’’ occurs in the absence of film rupture between

the hydrophilic alumina particles and bubbles, as has now

also been observed for the interaction of a bubble with a

Fig. 9 Experimental (symbols) and calculated (solid lines) induction

time values, tind, as a function of particle size and for different

solutions (KCl concentration/pH).

Fig. 10 Electrostatic (dotted lines), van der Waals (thick solid line)

and total DLVO interactions (solid lines) between hydrophilic a-Al2O3

particle and gas bubble at pH 10 (A) and 5.8 (B) calculated with

eqn (15) to (18) (see text for explanation).

This journal is c the Owner Societies 2010 Phys. Chem. Chem. Phys., 2010, 12, 14527–14533 14533

hydrophilic titania surface23,37 and postulated earlier by Derjaguin

and Dukhin12 in their ‘‘contactless’’ flotation model.

Conclusions

Results of single bubble flotation experiments have shown that

the collection and attachment efficiencies for hydrophilic

a-Al2O3 particles at pH values above the pHIEP were nearly

zero and were attributed to particle entrainment in the wake of

the rising bubble. At pH values below the pHIEP, where the

alumina particles are positively charged, much higher collec-

tion and attachment efficiencies were measured compared with

those above the pHIEP. Moreover, attachment efficiencies

increased with decreasing salt concentration and pH, indicating

that electrostatic interaction controls the attachment between

hydrophilic particles and gas bubbles. These attachment

efficiencies were in good agreement with those predicted by

the Dobby and Finch particle–bubble attachment model with

values of induction time obtained with this model close to

those obtained in the literature for similar size particles. The

results also indicate that the hydrophilic particles attach to

bubbles without film rupture in agreement with the original

‘‘contactless’’ flotation hypothesis of Derjaguin et al.12

Acknowledgements

The financial support of the University of South Australia

and CSIRO Process Science and Engineering is gratefully

acknowledged.

References

1 N. N. Rulyov, Colloids Surf., A, 2001, 192, 73.2 A. V. Nguyen and H. J. Schulze, Colloidal Science of Flotation,Marcel Dekker, New York, 2004.

3 J. Ralston, D. Fornasiero and R. Hayes, Int. J. Miner. Process.,1999, 56, 133–164.

4 B. V. Derjaguin, S. S. Dukhin and N. N. Rulev, Trans. - Inst. Min.Metall., 1960, 70, 221.

5 Z. Dai, S. Dukhin, D. Fornasiero and J. Ralston, J. ColloidInterface Sci., 1998, 197, 275–292.

6 Z. Dai, D. Fornasiero and J. Ralston, Adv. Colloid Interface Sci.,2000, 85, 231–256.

7 S. S. Dukhin, Kolloidn. Zh., 1982, 44, 431–441.8 K. Sutherland, J. Phys. Chem., 1948, 52, 394.

9 R. H. Yoon and G. H. Luttrell, Miner. Proces. Extr. Metall. Rev.,1989, 5, 101–122.

10 H. J. Schulze, Surfactant Sci. Ser., 1989, 47, 321–353.11 H. J. Schulze, Physico-chemical elementary processes in flotation: an

analysis from the point of view of colloid process engineeringconsiderations, Elsevier, Amsterdam, New York, 1984.

12 B. V. Derjaguin, S. S. Dukhin and N. N. Rulev, Surf. Colloid Sci.,1984, 13, 71–113.

13 G. S. Dobby and J. A. Finch, Int. J. Miner. Process., 1987, 21,241–260.

14 Z. Dai, D. Fornasiero and J. Ralston, J. Colloid Interface Sci.,1999, 217, 70–76.

15 Z. Dai, PhD thesis, University of South Australia, Adelaide,1998.

16 A. Jowett, in Fine particles processing, P. Somasundaran, AIME,AIMM, New York, 1980.

17 Y. Ye and J. D. Miller, Int. J. Miner. Process., 1989, 25, 199–219.18 A. Scheludko, B. V. Tochev and D. T. Gojadjiev, J. Chem. Soc.,

Faraday Trans. 1, 1976, 72, 2845.19 D. J. Hewitt, D. Fornasiero, J. Ralston and L. R. Fisher, J. Chem.

Soc., Faraday Trans., 1993, 89, 817–822.20 D. J. Hewitt, PhD thesis, University of South Australia, Adelaide,

1994.21 R. J. Pugh, M. W. Rutland, E. Manev and P. M. Claesson, Int. J.

Miner. Process., 1996, 46, 245–262.22 L. Parkinson and J. Ralston, J. Phys. Chem. C, 2010, 114,

2273–2281.23 M. Krasowska, G. Hanly, R. Dagastine, D. Fornasiero, R. Sedev,

K. W. Stockelhuber and J. Ralston, J. Phys. Chem. C, 2010,submitted for publication.

24 G. A. Parks, Chem. Rev., 1965, 65, 177–198.25 G. V. Franks, Colloids Surf., A, 2003, 214, 99–110.26 P. J. Eng, T. P. Trainor, G. E. Brown, G. A. Waychunas,

M. S. Newville, S. R. Sutton and M. L. Rivers, Science, 2000,288, 1029–1033.

27 J. C. Berg, Wettability, Marcel Dekker, New York, 1993.28 R. J. Good, J. Adhes. Sci. Technol., 1992, 6, 1269–1302.29 J. S. Hadamard, C. R. Acad. Sci., 1911, 152, 1735–1738.30 W. Rybczynski, Bull. Acad. Sci. Cracow Ser. A, 1911, 40–46.31 B. Pyke, D. Fornasiero and J. Ralston, J. Colloid Interface Sci.,

2003, 265, 141–151.32 G. S. Dobby and J. A. Finch, J. Colloid Interface Sci., 1986, 109,

493–498.33 M. Elimelech, J. Gregory, X. Jia and R. A. Williams, Particle

Deposition and Aggregation: Measurement, Modelling and Simulation,Butterworth-Heinemann, USA, 1995.

34 H. J. Schulze and C. Cichos, Z. Phys. Chem. (Leipzig), 1972, 251,252.

35 D. R. E. Snoswell, J. Duan, D. Fornasiero and J. Ralston, J. Phys.Chem. B, 2003, 107, 2986–2994.

36 J. Visser, Adv. Colloid Interface Sci., 1972, 3, 331–363.37 G. Hanly, PhD thesis, University of South Australia, Adelaide,

2008.